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An intelligent virtual fruit model focussing on quality attributes

By M. GNARD1, C. GIBERT1, C. BRUCHOU2 and F. LESCOURRET11

UR 1115 Plantes et Systmes de Culture Horticoles, INRA Domaine St Paul, Site Agroparc,Avignon Cedex 9, F-84914, France2UR 546 Biostatistiques et Processus Spatiaux, INRA Domaine St Paul, Site Agroparc, AvignonCedex 9, F-84914, France(e-mail: [email protected]) (Accepted 6 September 2009)

SUMMARYA process-based model of fruit quality expressing seasonal changes in several quality attributes of fruit (e.g., size,percentages of flesh, water, and sugar contents) on a fruit-bearing shoot (FBS) is presented as a contribution to theSMARTFRUIT work package in the framework of the EU Project, ISAFRUIT. Virtual experiments carried out onZphir peach (Prunus persica L. Batsch.) showed that fruit size at thinning had a dominant effect on fruit dry massand the percentage of flesh, whereas water potential had a large effect on both water content and sweetness. Fruit

load always had a moderate or small effect on quality attributes. An effect of assimilate supply from the rest of thetree to the FBS was also shown. Based on a wide range of time schedules of water supply, with alternate humid anddry periods of random length, the virtual fruit model suggested, in the case of the cultivar Suncrest, that fruitquality at harvest was essentially explained by the duration and humidity of the last period of the time schedule.Finally, during these experiments, the virtual fruit model behaved like a true system, and showed emergingproperties of both theoretical and practical interest. We draw conclusions on the opportunities that such a virtualfruit model offers for genetics, agronomy, and ecology, and discuss prospects for the extension of such virtual fruitand its incorporation into a virtual plant.

In Europe, the fruit supply chain is facing newchallenges such as increasing the consumption of fruitfrom sustainable production systems. Under current

European (EU) regulations, marketing organisations arerequired to improve quality all along the supply chain.Growers, who are key stakeholders in this chain, have toadapt their technical choices to present concerns.Scientists must help in this adaptation and in the designof new cropping systems by proposing tools that canimprove the decision-making processes. This is animportant objective of the ISAFRUIT project, andespecially SMARTFRUIT, a work package aimed atincreasing fruit quality by making use of availableresources such as water, light, and plant geneticpotential, in a smart and sustainable way.

Biological, technical, and economic models are usefulas complementary tools to support decision-making inagriculture. Biological models are especially necessary totake into account a wide range of criteria, and to allowfor rapid adaptation through evaluation, exploration,and learning (Boiffin et al., 2001).

To be able to help growers face unusual situations, anybiological model must, in our view, be process-based.Process-based models are more capable ofaccommodating unusual situations than empiricalmodels that can only be used under the particular rangeof conditions that were used to develop them.Moreover,only process-based models are able to integrate scientificknowledge from omics studies, or to consider, properly,all biotechnological advances.

In terms of the biological models applied to fruit

production, much work remains to be done, as fewcurrent models deal with fruit quality. Following thepioneering work of De Wit and Goudriaan (1978), most

process-based models that consider fruit have focussedon carbon relationships, leading to predictions of fruitgrowth in terms of dry weight (DW; Heuvelink andBertin, 1994). Few models have considered severalprocesses together, even though quality attributesdepend on many common and/or antagonisticprocesses. Clearly, the complexity of the fruit qualityprofile requires modelling of these underlyingprocesses, and their interactions, and must explicitlyconsider environmental variables that may betechnically driven (such as the leaf-to-fruit ratio), inorder to improve our understanding of the effect oftechnical changes. It is therefore imperative to designan intelligent model that can react to unusualgrowing conditions.

In this paper, we exemplify a multi-criterion, process-based model of fruit quality.This so-called virtual fruitwas based on the approach of Lescourret and Gnard(2005). We present examples of model development andits use to analyse environmental effects. We focus onpeach (Prunus persica L. Batsch.) and on attributes ofinterest to both growers and consumers, which are thetwo endpoints of the fruit supply chain and are thus keytargets for ISAFRUIT research. The attributes studiedwere: fresh weight (FW; g), which determines the pricepaid to the grower, the percentage of flesh in the fruit(g 100 g1), which determines the extent of the edible part

of the fruit, and water and sugar contents, whichdetermine fruit taste, which is the driving force ofconsumer satisfaction.*Author for correspondence.

Journal of Horticultural Science & Biotechnology (2009) ISAFRUIT Special Issue 157163

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An intelligent virtual fruit model

BRIEF OVERVIEW OF THE MODELA peach tree can be considered, from a fruit growers

viewpoint, as a collection of fruit-bearing shoots (FBS).Accordingly, our model represents FBS functions, with astrong focus on the fruit. The model is composed of fourexisting process-based models that describe the dryweight (DW; g) growth of the different components of

the FBS, including the fruit itself, sugar accumulation inthe fruit flesh, the growth in fruit FW (g), and fruitsurface conductance to water vapour diffusion. Themodel concerns stage III of fruit growth and runs on adaily basis.

The increase in DW was modelled as the carbonbalance of a FBS, according to the supply and demandapproach of Lescourret et al. (1998). The daily availablepool of C-assimilates consisted of leaf assimilation plus Ceventually mobilised from reserves, and possibly C fromthe rest of the tree. The level of C transfer depended onthe leaf-to-fruit ratio (i.e., the number of leaves pernumber of fruit) on both the FBS and the tree (Gibertet al ., data not shown). Leaf photosynthesis, at the FBSlevel, may be affected by feedback inhibition caused byleaf C-reserves. Carbon is allocated according to organdemand and priority rules. Maintenance respirationcosts, vegetative growth, and reproductive growth havefirst, second, and third-order priorities, respectively. TheC-demand for fruit growth depends strongly on sink sizeand activity, which means that fruit history plays animportant role in fruit C-demand. The latter alsodepends on developmental stage.The incoming C-flow isshared between the fruit flesh and the endocarp plusseed, according to an equation derived from an empiricalrelationship between endocarp plus seed DW and totalfruit DW. Using the compartmental approach of Gnard

et al. (2003), fruit flesh C is then partitioned into severalcompounds: four sugars (sucrose, sorbitol, glucose andfructose) in the case of peach. Other components wereconsidered as a whole (starch and structuralcarbohydrates), and respired CO2.The rates of change inthe amounts of C in the four sugar compounds aredescribed using a set of differential equations based onthe rate law of chemical kinetics (Chang, 2000), whichstates that the rate of a reaction is proportional to theconcentration of a reactant in the fruit.

According to the biophysical approach of Fishmanand Gnard (1998), the flow of water into the fruit isdriven by differences in the hydrostatic and osmoticpressures between the xylem or phloem, and the fruit.Fruit osmotic pressure induced by sugars is calculatedusing previous predictions of C compartmentation. Theincrease in fruit volume is assumed to be proportional tothe hydrostatic pressure according to Lockhart (1965).Fruit transpiration is calculated from the conductance ofthe skin to water vapour, and the difference in vapourpressure between the air and the fruit. The model ofGibert et al. (2005) was used to represent fruit surfaceconductance as the sum of the stomatal, cuticular, andcrack conductances.

Inputs into the fruit quality model were weather data(i.e., global radiation, temperature, and relative airhumidity), leaf and stem water potentials, and the

numbers of leafy shoots and fruit on the stem. Thequality attributes considered were fruit FW, thepercentage of flesh in the fruit (g 100 g1), water content,

the concentrations of different sugars, and a sweetnessindex (g sucrose equivalent 100 g1 flesh FW) computedas a linear combination of sugar concentrations, withsweetness ratings for each sugar (Kulp et al., 1991) ascoefficients.

HIGHLIGHTS OF MODEL DEVELOPMENT ANDUSEAnalysis of peach fruit dry weight growth

As stated above, an important step in the modellingwork was to analyse the C-demand of fruit for growth.Toexemplify this analysis, we used the late-maturingcultivar, Zphir as a case study. We used measurementsof fruit growth from trees with low fruit loadscorresponding to 89 separate fruit growth curves. Furtherdetails of the growing conditions and sampling methodscan be found in Gibert et al. (2007). Such non-limiting Cconditions, under which fruit growth was generallyreferred to a potential growth because fruit demandwas satisfied throughout fruit development, are suitableto estimate parameters in the equation describing fruitC-demand. Different equations were tested. A logisticequation was chosen to describe potential fruit growthfrom 700 degree days (C d) after bloom to harvest(1,800 C d).The equation used was:

DW(to)DW(t) =

1 e(P2 (t P3))

where DWwas the fruit dry weight (g), and , P2 and P3were parameters. Time twas in degree days (t0 = 700 Cd). The product DW(t0) is the maximum DW that a

fruit can reach.The goodness-of-fit of the equation was satisfying.Themodel was able to predict the variability in growth forlow-fruit-load trees by considering only variability inDW at 700 C d (Figure 1A).

Applying the potential fruit growth model directlyto fruit on high fruit load trees led to an overestimationof fruit growth (Figure 1B). This showed that the initialDW, which was the only source of variation in thepotential fruit growth model, could not, alone, explainall of the variation in fruit growth. When included in aglobal fruit model that explicitly considered C-supply asa limiting driving force, the potential fruit growthequation correctly predicted fruit growth on high fruitload trees (Figure 1C).

The virtual fruit model fits well to the quality dataFigure 2 shows the time-course of quality attributes

during fruit growth, either monitored directly orsimulated by the virtual fruit model, in the case of themid-season peach cultivar, Suncrest. Peaches weregrown on girdled FBS isolated from the rest of the tree,with high or low fruit loads. Further details of the data,and the sampling and analysis procedures can be foundin Gnard and Souty (1996).

The model accounted for the increase in fruit growthfor low-load FBS compared to high-fruit-load FBS. The

observations indicated that water contents and thepercentage of flesh in the fruit increased over time, andthat their levels were higher and lower for high-load than

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M. GNARD, C . GIBERT, C . BRUCHOU and F. LESCOURRET

for low-load FBS, respectively. The model reproducedthese unpredictable patterns, which was the firstindication of its intelligence. Figure 2 alsodemonstrates that the model correctly represented thekinetics of the different sugars and the hierarchy of theirlevels at harvest, with the highest level for sucrose,

followed by glucose, fructose, then sorbitol, as well as theeffect of fruit load on sugars, with higher sweetnessvalues for low fruit loads.

Virtual experiments on environmental factorsIn the first series of virtual experiments, the virtual

fruit model was used to analyse the effect of DW at thefruit thinning stage, fruit load of the FBS, and assimilatesupply from the tree, on fruit growth (DW) in the case ofZphir peach. For the two first factors (indicative ofthinning time and intensity, respectively) we used thecurrent range of variations in this cultivar: namely 3 8 gfor fruit DW at thinning, and one to six for the numberof fruit per FBS. For the third factor, assimilates wereallowed to be transferred from the tree to the FBS, ornot, which mimics girdling at the basis of the stem tosuppress phloem flow. The simulations showed largeeffects of all three factors. The effect of fruit load wasmuch less when the FBS assimilate supply was suppliedby the tree (Figure 3).

Assuming that the FBS was supplied by the tree, andusing a variance decomposition procedure, the virtualfruit model was used to analyse the effect of fruit DW atthe fruit thinning stage, the fruit load of the FBS, andplant water status (indicative of irrigation strategy anddepicted by stem water potential), on fruit quality atharvest in Zphir peach.The ranges of variation in fruit

DW at thinning and fruit load per FBS were as statedabove. The mean stem water potentials (0.73 MPa to0.57 MPa) also corresponded to commonly-used

agronomic standards. All three factors affected fruitquality without any strong interactions between them(Table I). Fruit DW at thinning had a large and positiveeffect on fruit size and on the percentage of flesh in thefruit at harvest.Similar results have been found in mangofruit (Lchaudel et al., 2005). Fruit size at thinningprovides a good indicator of cell numbers in the fruitflesh, which is a major component of the potential forfruit growth (Westwood, 1967).

Fruit load always had a moderate or small effect onfruit quality attributes, as exemplified by the previousvirtual experiment, probably because the C supply from

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FIG. 1

Fruit growth curves (dry weight in g) of 88 peach fruit (Zphir)measured on low fruit load trees in 2004 (Panel A), 89 peach fruits(Zphir) measured on high fruit load trees in 2004 (Panel B), 214peach fruit (Zphir) measured on high fruit load trees in 2005(Panel C). The points are the measurements and the lines are theadjustment using the logistic model (Panel A), predictions with thelogistic model (Panel B), and predictions using the virtual fruit model

(Panel C).

800 1,200 1,600 2,000 800 1,200 1,600 2,000

800 1,200 1,600 2,000

FIG. 2Time-courses of various quality attributes in peach fruit (Suncrest)

grown at high (six leaves per fruit; Panels A - G) or low (18 leaves perfruit; Panels H - N) fruit load.The symbols and bars represent the meansand standard deviations of the measurements (n = 5) and the lines are

the predictions using the virtual fruit model.

50

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weight(g)

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content(%)

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the tree compensated for the local C deficit, and becausefruit DW at thinning had a dominant effect on the C-demand of fruit in Zphir peach. Stem water potentialhad a large and positive effect on fruit water content,anda negative effect on sweetness, which was expectedthrough the process of dilution resulting from the supplyof water.

In the final series of virtual experiments, a wide rangeof time schedules of water supply was simulated usingSuncrest peach fruit, starting from the observation thatfruit crops often encounter alternate dry and humidperiods, the duration of which can be highly variablebecause of unpredictable weather events, or varioustechnical constraints. Within a framework of alternatedry and humid periods, this virtual experiment wasaimed at answering the following questions: is there arelationship between time schedules of water supply andfruit quality at harvest? And, if so, which trait or traits inthe time schedules was responsible for such arelationship? To address these questions, two series of

100-time schedules of water supply, each composed of sixsuccessive periods of alternating and contrasting waterconditions, were set up. The periods were of randomlength, but the sum of the durations of the six periods ineach time schedule was fixed by the duration of fruitgrowth. In the first series, the first period was dry (i.e., awater deficit represented by a mean stem water potentialof -0.8 MPa). In the second series, the first period wasirrigated by an irrigation system or by rainfall (i.e.,normal water conditions as represented by a mean stemwater potential of -0.5 MPa). The alternation of waterconditions meant that each dry period was followed by ahumid period, and vice versa.

Figure 4 shows these results of the experiments fortwo quality attributes: FW and fruit sweetness.The time-course of quality attributes fluctuated greatly, indicatingthe very reactive behaviour of the virtual fruit model.The analyses, undertaken separately for each of the twoseries described above, demonstrated that there was norelationship between the global pattern of time

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TABLE IComponents of variance in Zephir peach fruit quality attributes (% of total variance) as a function of fruit dry weight at thinning [DW (t0)], fruit load,

and plant water status (),simulated using the virtual fruit model

Factor Fruit dry weight Percentage of flesh in the fruit Water content Sweetness

DW (t0) 76.8 79.1 20.4 11.9Load 6.6 3.2 4.0 1.5 9.1 13.8 69.8 79.7DW (t0) Load 6.8 0.9 0.2 0.9DW (t0) 0.5 1.8 0.0 0.1

Load 0.2 1.2 5.4 5.6Residuals 0.0 0.1 0.2 0.2

FIG. 3Simulated effects of fruit dry weight [DW (t0)] and fruit load at thinning (1 6 fruits per fruit-bearing shoot) on dry weight growth in peach fruit

Zphir with no assimilate supply from the tree (Panels A, C), or with assimilate supply from the tree (Panels B, D).

No assimilatesupply from

the tree

Assimilatesupply from

the tree

DW(to) = 3g DW(to) = 8g

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schedules of water supply and fruit quality at harvest(data not shown). The duration of each of the six periods,the total duration of the dry periods, and the totalduration of the humid periods, were then tested ascandidate variables. This exploratory analysisdemonstrated that fruit quality at harvest couldessentially be explained by the duration of the lastperiod of the time schedule.The correlation was positivefor FW and negative for sweetness in the case of timeschedules that started with a dry period and ended witha humid period; and, conversely, negative for FW andpositive for sweetness in the case of time schedules thatstarted with a humid period and ended with a dry period.

These three virtual experiments clearly demonstratethat the virtual fruit model was intelligent. It was ableto reveal behaviours that would have been unpredictablewhen considering only the basic components of themodel. It suggested that the main effect of alternate dryand humid periods was caused by the duration of the lastperiod, which is of both theoretical and practical interest.It exemplifies the ability of the virtual fruit model todirect research into unknown abilities of the fruit system.

CONCLUSIONS AND PROSPECTS

In this study, we have shown the relevance of a multi-criterion, process-based model of fruit quality, a virtualfruit model, by analysing environmental effects by

means of virtual experiments. During these experiments,the virtual fruit model behaved like a true system, andshowed emerging properties of both theoretical andpractical interest. The model is therefore a usefulcontribution to SMARTFRUIT, within the ISAFRUITProject, which aims to produce conceptual andmethodological research tools to promote fruitconsumption in Europe. It may also be especially helpfulfor applied research in agronomy and genetics.

The virtual fruit model provides a future opportunityfor agronomy. It may help us to understand futureexperimental results not yet documented. Also,performing virtual experiments provides an opportunityto control factors that are difficult to control in theorchard, such as fruit size at thinning.

The virtual fruit model also provides an opportunityfor genetics research. Geneticists still encounter twomajor difficulties. First, quality attributes that arebreeding targets result from many overlapping processesand are thus controlled by many genes. Second, thesecharacters are under the influence of the environment.This often results in strong genotype environmentinteractions, which make genetic analyses, and theirapplications to breeding, difficult. Studying aquantitative attribute via the virtual fruit model made it

possible to deal with both difficulties simultaneously.Instead of looking for QTLs that control an attributedirectly, it is more efficient to look for QTLs that control

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FIG. 4Virtual experiment on the effects of various time schedules of water supply, with alternate periods of normal or water stress conditions of randomlength, on the fresh weight (FW) and sweetness of Suncrest peach fruit. Panels A, B, time-course of quality attributes for 100-time schedules. Theupper thick line in Panel A and the lower thick line in Panel B represent the case where the water supply was normal throughout fruit development.The lower thick line in Panel A and the upper thick line in Panel B represent the case where water supply was reduced throughout fruit development.Panels C F, relationships between the duration of the last period of drought or water supply and the two quality attributes at harvest (smoothedcurves). Panels C, D, time schedules that started with a dry period and ended with a humid period. Panels E, F, time schedules started with a humid

period and ended with a dry period.

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(normal irrigation; d)

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tness(%)

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tness(%)

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the model parameters, because they are assumed to beindependent of the environment. This approach wasapplied to peach fruit by Quilot et al. (2005a,b).Throughout studies on the co-location of QTLs forparameters and QTLs for attributes, the physiologicalmeanings of QTLs for attributes have been proposed.This opens the way to design in silico ideotypes adapted

to given requirements, which may constitute a basis forfuture breeding.In addition, the virtual fruit model may provide an

opportunity for ecology research. It may help torenewing studies on quantitative interactions betweendiseases or pests, and crops, by offering the possibility togo beyond classical yield losses (Gutierrez and Curry,1989; Gutierrez et al., 1991; Rossing, 1991) and to takequality losses into account. It may also strengthen studieson qualitative interactions, by considering hostsusceptibility, that may affect the physical characteristicsand chemical composition of fruit, including secondarymetabolites that play a major role in defense (Toms-Barbern and Espn, 2001; Cipollini et al., 2004;Dudareva and Negre, 2005).

In its present form, however, the virtual fruit modelhas some limitations. First, it is only for fruit.Nevertheless, fruit quality varies greatly, especially at thetree level (Audergon et al., 1993; Habib et al., 1991),under the influence of different horticultural practices.As research on virtual plants is expanding rapidly, we arecurrently incorporating the virtual fruit model into avirtual plant model that is able to react to horticultural

operations (Gnard et al. , 2008). More generally,incorporating the virtual fruit model into a crop modelwill be valuable to simulate the combined effects ofchanges in climate, the development of pests that affectfruit directly or indirectly, genotype, and horticulturaloperations, on quality attributes. This should providehelpful information to improve crop breeding and crop

management processes. Second, the virtual fruit modelshould be extended to include other fruit attributes.Thecurrent model considers Stage III of fruit growth, butfeatures of cell division determine the fate of a fruit(Bertin et al., 2003). The range of quality attributesstudied does not yet include secondary metabolites, suchas natural defense components, or components that areadvocated by national nutrition and health policies, andare key targets of the ISAFRUIT Project.Modelling, andvirtual or real experiments, should progresssimultaneously to overcome these limitations (Bertinet al ., 2006).A modelling framework has been proposedto organise such research for a new generation of virtualfruit (Gnard et al., 2007).

The ISAFRUIT Project is funded by the EuropeanCommission under Thematic Priority 5 Food Qualityand Safety of the 6th Framework Programme of RTD(Contract No. FP6-FOOD-CT-2006-016279).

Disclaimer: Opinions expressed in this publicationmay not be regarded as stating an official position of theEuropean Commission.

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